Boundary Value Problems
Volume 2005 (2005), Issue 2, Pages 181-199

Multidimensional Kolmogorov-Petrovsky test for the boundary regularity and irregularity of solutions to the heat equation

Ugur G. Abdulla

Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, FL, USA

Received 25 August 2004

Copyright © 2005 Ugur G. Abdulla. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of N+1 (N2) for the diffusion (or heat) equation. The result implies asymptotic probability law for the standard N-dimensional Brownian motion.